# InfoCoBuild

## Numerical Methods

Numerical Methods. Instructors: Dr. Ameeya Kumar Nayak and Dr. Sanjeev Kumar, Department of Mathematics, IIT Roorkee. This course is a basic course offered to UG student of Engineering/Science background. It contains solution of system of linear equations, roots of nonlinear equations, interpolation, numerical differentiation and integration. It plays an important role for solving various engineering sciences problems. Therefore, it has tremendous applications in diverse fields in engineering sciences. (from nptel.ac.in)

 Introduction to Error Analysis and Linear Systems

 Lecture 01 - Introduction to Error Analysis and Linear Systems Lecture 02 - Gaussian Elimination with Partial Pivoting Lecture 03 - LU Decomposition Lecture 04 - Jacobi and Gauss Seidel Methods Lecture 05 - Iterative Methods Lecture 06 - Introduction to Nonlinear Equations and Bisection Method Lecture 07 - Regula Falsi and Secant Methods Lecture 08 - Newton-Raphson Method Lecture 09 - Fixed Point Iteration Method Lecture 10 - System of Nonlinear Equations Lecture 11 - Introduction to Eigenvalues and Eigenvectors Lecture 12 - Similarity Transformations, Singular Value Decomposition, Gershgorin Theorem Lecture 13 - Jacobi Method for Computing Eigenvalues Lecture 14 - Power Method Lecture 15 - Inverse Power Method Lecture 16 - Introduction to Interpolation Lecture 17 - Interpolation: Some Basic Operators and their Properties Lecture 18 - Interpolation: Newton's Forward/Backward Difference Formula Lecture 19 - Interpolation: Error in Approximating a Function by a Polynomial using Newton's Forward/Backward Difference Formula Lecture 20 - Interpolation: Solving Problems using Newton's Forward/Backward Difference Formula Lecture 21 - Interpolation: Central Difference Formula Lecture 22 - Interpolation: Lagrange's Interpolation Formula with Examples Lecture 23 - Interpolation: Divided Difference Interpolation with Examples Lecture 24 - Interpolation: Hermite's Interpolation Formula with Examples Lecture 25 - Introduction to Numerical Differentiation Lecture 26 - Numerical Differentiation based on Lagrange's Interpolation Formula Lecture 27 - Numerical Differentiation based on Divided Difference Formula Lecture 28 - Numerical Differentiation: Maxima or Minima of a Tabulated Function Lecture 29 - Numerical Differentiation based on Finite Difference Operators Lecture 30 - Numerical Differentiation: Method of Undetermined Coefficients with Unequal Intervals Lecture 31 - Methodology of Numerical Integration and Rectangular Rule Lecture 32 - Numerical Integration: Quadrature Formula and Trapezoidal Rule with Associated Errors Lecture 33 - Numerical Integration: Simpson's 1/3rd Rule with Associated Errors Lecture 34 - Numerical Integration: Composite Simpson's 1/3rd Rule and Simpson's 8/3th Rule Lecture 35 - Numerical Integration: Gaussian-Legendre 2-point and 3-point Formula with Examples Lecture 36 - Introduction to Ordinary Differential Equations Lecture 37 - Numerical Methods for ODEs: Picard's Method, Euler's Method Lecture 38 - Numerical Methods for ODEs: Taylor Series Method and Euler's Modified Method Lecture 39 - Numerical Methods for ODEs: Runge-Kutta Method Lecture 40 - Numerical Methods for ODEs: Multi-Step Method

 References Numerical Methods Instructors: Dr. Ameeya Kumar Nayak and Dr. Sanjeev Kumar, Department of Mathematics, IIT Roorkee. This course covers solution of system of linear equations, roots of nonlinear equations, interpolation, numerical differentiation and integration.